Suppose we have to find a diagonal matrix similar to a symmetric matrix... Is it possible to just have the diagonal matrix which can be generated by congruent operations and say the matrix is similar to the diagonal matrix generated by the congruent operation?
2026-04-04 14:47:48.1775314068
Diagonalisation of symmetric Matrix
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For a symmeric matrix the diagonalitazion correspond to:
$$D=S^{-1}AS$$
Thus of course D can be obtained by row and columns operations. However you need to know the diagonal entries i.e. the eigenvalues.